Effect of edge dislocations on structural and electric properties of 4H-SiC J.La_zewski,P. T. Jochym, P. Piekarz, M. Sternik, K. Parlinski, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Cracow, Poland J. Cholewi´nski,P. Dlu_zewski Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawi´nskiego5b, 02-106 Warsaw, Poland S. Krukowski Institute of High Pressure Physics, Polish Academy of Sciences, Soko lowska 29/37, 01-142 Warsaw, Poland Interdisciplinary Centre for Materials Modelling, Warsaw University, Pawi´nskiego5a, 02-106 Warsaw, Poland E-mail: [email protected] Abstract. The paper presents a study of two full-core, edge dislocations of opposite Burgers vectors in 4H-SiC, conducted using the first-principles density functional theory methods. We have determined the creation energy of the dislocations as a function of distance between their cores. The radial distribution function has been applied to examine strong impact of the dislocations on the local crystal structure. The analysis of the electronic structure reveals mid-gap levels induced by broken atomic bonds in the dislocation core. The maps of charge distribution and electrostatic potential have been calculated and the significant decrease of the electrostatic barriers in the vicinity of the dislocation cores has been quantified. The obtained results have been discussed in the light of available experimental data. PACS numbers: 71.30.+h, 71.38.-k, 64.70.Kb, 75.50.Gg arXiv:1502.00309v1 [cond-mat.mtrl-sci] 1 Feb 2015 Effect of edge dislocations on structural and electric properties of 4H-SiC 2 Introduction The Silicon Carbide (SiC), a wide band gap semiconductor, is a promising material for high-voltage and high-frequency nanoelectronic devices [1, 2]. Very good operational quality of SiC results from high values of breakdown voltage (≈ 106 V/cm), high charge carrier mobility, high temperature stability and high thermal conductivity [3]. Additionally, this material has very good mechanical properties and resistance to radiation damage. Unfortunately, the electronic properties of epitaxial layers strongly depend on the material quality. The presence of intrinsic defects and impurities which arise during crystal growth process substantially limit applications of SiC. Dislocations are the main crystal defects in SiC. They deteriorate the performance of high electric field devices such as Shottky and p-n diodes [4, 5]. Two typical components of dislocations with the direction along [0 0 0 1] are the screw and edge dislocations with 1 ¯ Burgers vectors [0 0 0 1] and 3 [2 1 1 0], respectively. The standard density of dislocations observed in the good quality 4H-SiC epilayers reaches 103 cm−2 [6]. The electrical characteristics of 4H-SiC photodiodes reveal that the screw and edge dislocations reduce the breakdown voltage by 3:5% and 2%, respectively, and increase the leakage currents compared to systems without crystal defects [7]. Dislocations also influence transport properties of 4H-SiC by increasing recombination activity [8] and reducing the diffusion length in the material [9]. Various mechanisms are responsible for modifications of electronic structure in the presence of dislocations. In the dislocation core, the broken bonds give rise to acceptor levels within the band gap and make this region electrically active [10, 11]. Dislocations also act as trapping centres and sources for point defects [12]. In the vicinity of the core, the strain field may induce additional states located near the conduction band edge [13]. In epitaxial SiC, several gap levels have been detected using the deep-level transient spectroscopy (DLTS) and their connection with the intrinsic defects have been analysed [14, 15]. The structural properties of dislocations have been previously studied theoretically in very few materials using both empirical potentials [16] and ab initio methods based on the density functional theory (DFT) [17, 18, 19, 20]. The DFT provides tools that allow one to study changes in electronic structure induced by dislocations [21]. Such computations revealed that the dislocation core in GaN induces deep-gap states [22, 23], which strongly influence the electronic and optical properties of this semiconductor [24]. The point defects such as vacancies and oxygen dopants can be easily trapped at the core of the edge dislocations providing additional mid-gap states [22, 25]. The influence of partial dislocations on the structural and electronic properties have been investigated in the pure SiC [26] and crystals doped with impurity atoms [27]. However, to our best knowledge, electronic properties of the full-edge dislocation has not been studied with ab initio methods yet. In this work we study the changes in the crystal structure and electronic properties of 4H-SiC induced by the edge dislocation. We analyse in detail the local lattice Effect of edge dislocations on structural and electric properties of 4H-SiC 3 distortion by means of the radial distribution function (RDF) { the density of atoms in the spherical shell around given atom averaged over whole structure [28, 29, 30]. The calculations disclose significant redistribution of charges and electrostatic potential in the region of the dislocation core. The electronic states located in the insulating gap, arising from the dislocation core atoms, show a very weak dispersion in the perfect correlation with the distribution of charges in the distorted region. Estimated minimal electrostatic barriers for ideal and distorted systems throw a new light on the decrease of the breakdown voltage in the defected 4H-SiC crystal. Methods All calculations have been executed with the Vienna Ab-Initio Simulation Package (VASP) [31, 32] using the full-potential projector-augmented wave method [33, 34] within the generalised-gradient approximation (GGA) [35, 36, 37]. The following valence base configurations have been included: Si 3s23p2 and C 2s22p2. The integration over the k-point space has been performed over the 2 × 2 × 2 Monkhorst-Pack mesh [38] and the energy cut-off for the plane waves expansion was equal to 500 eV. The structures of ideal and defected crystals have been fully optimised (with respect to lattice parameters, stresses, and internal degrees of freedom) in the supercells consisting of 8×6×1 primitive unit cells, containing 384 and 346 atoms, which correspond to 25A˚×19A˚×10A˚ and 22A˚×19A˚×10A˚ crystal volumes, respectively. We have used the conjugate gradient technique with the energy convergence criteria set at 10−8 eV and 10−5 eV for the electronic and ionic iterations, respectively. Results Crystal structure The pure 4H-SiC crystal structure has been reproduced correctly with the lattice constants a = 3:095 A˚ and c = 10:132 A,˚ which are very close to experimental values that amount to 3.073 A˚ and 10.053 A,˚ respectively. To fulfil the periodic boundary conditions we consider two full-core edge dislocations with opposite Burgers vectors 1 ¯ 1 ¯ ¯ 3 [2 1 1 0] and 3 [2 1 1 0], inserted into the system using Visual Editor of Crystal Defects (VECDs) [39]. It involves removal of 38 selected atoms (19 SiC molecules) changing the total number of them, which has been taken into account in all comparisons to the ideal structure. Nevertheless, the relaxed crystal volume noticeably increases (by about 1%) due to the local destruction of hexagonal close-packed structure. However, since the supercell is big enough, the elongation of the average near neighbour bond is below 0.5% in comparison to its length in the ideal system. The creation energy per unit length of a single edge dislocation has been calculated as a function of distance between their cores using the following formula [23]: 0 e = (E − E0)=2c; Effect of edge dislocations on structural and electric properties of 4H-SiC 4 Figure 1. Off-bottom (upper panel) and top (lower panel) view of the optimised crystal structure of 4H-SiC with two full-core edge dislocations. Both dislocation edges (I and II) have been distinguished by colour. 0 where E is the energy of the system with a pair of dislocations (346 atoms), E0 is the ground state energy of the undisturbed system normalised to the same number of formula units. For relative distance between cores equal to 6.73 A˚ we have obtained e = 2:17 eV/A˚ per supercell. Additionally, it has been found that e increases for larger distances due to attractive force between two dislocations of opposite sign [40]. The Peierls energy barrier between two states of dislocation core at adjacent lattice nodes along the common glide plane is very low. Therefore, to prevent the annihilation of defects during optimisation process we have trapped both dislocations by pinning their cores at different glide planes. The optimised 4H-SiC structure with two edge dislocations is presented in Fig. 1. The positions of dislocation lines have been marked by atoms distinguished by different colour. Carrying out crystal structure relaxation, without any symmetry constrains, we have found that it tends to self-recover { reconstructing as much as possible of pure 4H-SiC coordinations and so gathering most of the disorder to one of the dislocation cores (I in Fig. 1). To analyse the influence of the dislocation on its nearest neighbourhood, the RDF for the dislocation dipole has been calculated and analysed. In Fig. 2 one can immediately notice that the introduction of the edge dislocation disturbs hexagonal close-packed structure which results in slight increase of the near neighbour and next near neighbour distances visible as shift from pure 4H-SiC positions (dashed lines). We discovered that each coordination shell can be fitted with a two-component function (two Gaussian lines with parameters collected in Table 1): the central part with small Effect of edge dislocations on structural and electric properties of 4H-SiC 5 15 15 first coordination shell second coordination shell calculated RDF dislocation core region 10 ordered region fit 10 total fit RDF 5 5 0 0 1.8 2.0 3.0 3.2 r (Å) Figure 2.